RWW Taylor gave a marvelously complete algebraic response to the issue
raised in this thread. Thanks, RWW!
Others {Donna, Wayne, ...} also have added their personal view. Vern, for
example, gives us the caution to consider what is appropriate for the
moment.
my two cents: zero is the intersection of the Real numbers (line) and the
Imaginary numbers (line). Thus zero can be considered real if that suits
your purpose, or imaginary if that is appropriate.
The real numbers are just a line through the complex numbers plane, but it
has a natural order that numbers in the plane lack.
On that ordered line, zero can be viewed as nonnegative or nonpositive or
BOTH! When we teach lower bounds on the zeros of polynomials using the
synthetic division schema [DO WE STILL DO THAT???], we regard zero as
WHICHEVER it has to be.
matthewg@goliath.sunyocc.edu
George E. Matthews, Onondaga Community College, Syracuse, NY13215
(315) 469-2381
PS. The NYSMATYC Summer Institute / AMATYC Regional Conference just held
at Dutchess County Community College suggests that the technique of
synthetic division be de-emphasized in precalculus. So I have a partial
answer to my question above.
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